Related papers: Linear canonical transformations and quantum phase…
Quantum canonical transformations corresponding to time-dependent diffeomorphisms of the configuration space are studied. A special class of these transformations which correspond to time-dependent dilatations is used to identify a…
An assessment is given as to the extent to which pure unitary evolution, as distinct from environmental decohering interaction, can provide the transition necessary for an observer to interpret perceived quantum dynamics as classical. This…
In this paper we show that there is a link between the combinatorics of the canonical basis of a quantized enveloping algebra and the monomial bases of the second author arising from representations of quivers. We prove that some…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the…
The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. Physically, what lie at the foundation of any formalism for quantization in curved…
With the goal in mind of deriving a method to compute quantum corrections for the real-time evolution in quantum field theory, we analyze the problem from the perspective of the Wigner function. We argue that this provides the most natural…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
A superintegrable generalization of the classical and quantum Zernike systems is reviewed. The corresponding Hamiltonians are endowed with higher-order integrals and can be interpreted as higher-order superintegrable perturbations of the 2D…
We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of…
We review the problem of state reconstruction in classical and in quantum physics, which is rarely considered at the textbook level. We review a method for retrieving a classical state in phase space, similar to that used in medical imaging…
A recent development of the studies on classical and quasi-classical properties of supersymmetric quantum mechanics in Witten's version is reviewed. First, classical mechanics of a supersymmetric system is considered. Solutions of the…
In this work we study the Wigner functions, which are the quantum analogues of the classical phase space density, and show how a full rigorous semiclassical scheme for all orders of \hbar can be constructed for them without referring to the…
We develop a systematic classical framework to accommodate canonical quantization of geometric and matter perturbations on a quantum homogeneous isotropic flat spacetime. The existing approach of standard cosmological perturbations is…
The evaluation of multi-loop Feynman integrals is one of the main challenges in the computation of precise theoretical predictions for the cross sections measured at the LHC. In recent years, the method of differential equations has proven…
We describe a quantum system consisting of a one-dimensional linear chain of n identical harmonic oscillators coupled by a nearest neighbor interaction. Two boundary conditions are taken into account: periodic boundary conditions (where the…
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
A quantum version of the action principle is formulated in terms of real parameters of a wave functional. The classical limit of the quantum action of a harmonic oscillator is obtained.
A common approach to minimizing the cost of quantum computations is by transforming a quantum system into a basis that can be optimally truncated. Here, we derive classical equations of motion subjected to similar unitary transformations,…